Spectral Stability of Weak Relaxation Shock Profiles

Using a combination of Kawashima- and Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems. This extends previous results obtained by Plaza and Zumbrun [8] by singular perturbation techniques under an additional technical assumption, namely, that the background equation be noncharacteristic with respect to the shock.